Research Database

This paper formalizes and quantifies the secular stagnation hypothesis, defined as a persistently low or negative natural rate of interest leading to a chronically binding zero lower bound (ZLB). Output-inflation dynamics and policy prescriptions are fundamentally different from those in the standard New Keynesian framework. Using a 56-period quantitative life cycle model, a standard calibration to US data delivers a natural rate ranging from -1.5% to -2%, implying an elevated risk of ZLB episodes for the foreseeable future. We decompose the contribution of demographic and technological factors to the decline in interest rates since 1970 and quantify changes required to restore higher rates.

The existence of fixed points for monotone maps on spaces of measures is established. The case of monotone Markov processes is analyzed and a uniqueness and global stability condition is developed. A comparative statics result is presented and the problem of approximation to the invariant distribution is discussed. The conditions of the theorems are verified for the cases of Optimal Stochastic Growth and Industry Equilibrium.

We describe a model for calculating the optimal quantity of debt and then apply it to the U.S. economy. The model consists of a large number of infinitely-lived households whose saving behavior is influenced by precautionary saving motives and borrowing constraints. This model incorporates a different role for government debt than the standard representative agent growth model and captures different trade-offs between the benefits and costs of varying its level. Government debt enhances the liquidity of households by providing additional assets for smoothing consumption (in addition to claims to capital) and effectively loosening borrowing constraints. By raising the interest rate, government debt makes assets less costly to hold and more effective in smoothing consumption. However, the implied taxes have wealth distribution, incentive, and insurance effects. Further, government debt crowds out capital (via higher interest rates) and lowers per capita consumption. Our quantitative analysis suggests that the crowding out effect is decisive for welfare. We also describe variations of the model which permit endogenous growth. It turns out that even with lump sum taxes and inelastic labor, government debt as well as government consumption have growth rate effects, thereby implying large welfare gains from reducing the level of debt.

This note presents a model whose competitive equilibrium can be consistent with the observation that current labor market conditions affect the well-being of new entrants more than they do that of senior workers. The model uses the notion that new entrants are not around soon enough to participate in risk-sharing contingent on the shocks that determine the equilibrium marginal products of first-period employment. This timing notion is formalized using a stochastic overlapping generations model.

A problem facing the United States and many other countries is how to finance retirement consumption as the number of their workers per retiree falls. The problem with a savings for retirement systems is that there is a shortage of good savings opportunities given the nature of most current tax systems and governments’ limited ability to honor the debt it issues. We find that eliminating capital income taxes will greatly increase saving opportunities and make a savings-for-retirement system feasible with only modest amount of government debt. The switch from a system close to the current U.S. retirement system, which relies heavily on taxing workers’ incomes and making lump-sum transfers to retirees, to one without income taxes will increase the welfare of all birth-year cohorts alive today and particularly the welfare of the yet unborn cohorts. The equilibrium paths for the current and alternative policies are computed.

We examine an otherwise standard model of capital accumulation to which spatial separation and limited communication create a role for money and shocks to portfolio needs create a role for banks. In this context we examine the existence, multiplicity, and dynamical properties of monetary equilibria with positive nominal interest rates. Moderate levels of risk aversion can lead to the existence of multiple monetary steady states, all of which can be approached from a given set of initial conditions. In addition, even if there is a unique monetary steady state, monetary equilibria can be indeterminate, and oscillatory equilibrium paths can be observed. Thus financial market frictions are a potential source of both indeterminacies and endogenously arising economic volatility.

We also consider the consequences of monetary policy actions that rearrange the composition of government liabilities. Contractionary monetary policy activities can have complicated consequences, depending especially on the nature of the steady state equilibrium that obtains when there are multiple steady states. Under plausible conditions, however, a permanent contractionary change in monetary policy raises both the nominal rate of interest and the rate of inflation, and reduces long-run output levels. Thus liquidity provision by a central bank—just as by the banking system as a whole—can be growth promoting. Loose monetary policy also is conducive to avoiding development trap phenomena.

This paper proposes a theory of foreign reserves as macroprudential policy. We study an open economy model of financial crises, in which pecuniary externalities lead to over-borrowing, and show that by accumulating international reserves, the government can achieve the constrained-efficient allocation. The optimal reserve accumulation policy leans against the wind and significantly reduces the exposure to financial crises. The theory is consistent with the joint dynamics of private and official capital flows, both over time and in the cross section, and can quantitatively account for the recent upward trend in international reserves.

We show that short and long nominal interest rates are independent monetary policy instruments. The pegging of both helps solving the problem of multiplicity that arises when only short rates are used as the instrument of policy. A peg of the nominal returns on assets of different maturities is equivalent to a peg of state-contingent interest rates. These are the rates that should be targeted in order to implement unique equilibria. At the zero bound, while it is still possible to target state-contingent interest rates, that is no longer equivalent to the target of the term structure.

We study a model with heterogeneous producers that face collateral and cash-in-advance constraints. These two frictions give rise to a nontrivial financial market in a monetary economy. A tightening of the collateral constraint results in a recession generated by a credit crunch. The model can be used to study the effects on the main macroeconomic variables, and on the welfare of each individual of alternative monetary and fiscal policies following the credit crunch. The model reproduces several features of the recent financial crisis, such as the persistent negative real interest rates, the prolonged period at the zero bound for the nominal interest rate, and the collapse in investment and low inflation in spite of the very large increases in liquidity adopted by the government. The policy implications are in sharp contrast to the prevalent view in most central banks, which is based on the New Keynesian explanation of the liquidity trap.

This article asks whether or not the overall welfare of U.S. residents would be greater if U.S. federal law prohibited state governments from offering tax breaks to particular businesses. The answer of a formal model is yes, making such tax breaks illegal could increase a summary measure of total welfare in the economy. According to the model, the policy could increase welfare because it would increase the tax revenue collected from capital agents, and that revenue could finance an increase in spending on public goods. The policy would also spread the tax burden more evenly in the economy and so reduce the deadweight loss of taxation per dollar collected. In addition, the policy would lead to a more efficient pattern of industry locations in the economy.

We develop and calibrate a search-theoretic model of the labor market in order to forecast the evolution of the aggregate US labor market during and after the coronavirus pandemic. The model is designed to capture the heterogeneity of the transitions of individual workers across states of unemployment and employment and across different employers. The model is designed also to capture the trade-offs in the choice between temporary and permanent layoffs. Under reasonable parametrizations of the model, the lockdown instituted to prevent the spread of the novel coronavirus is shown to have long-lasting negative effects on unemployment. This is because the lockdown disproportionately disrupts the employment of workers who need years to find stable jobs.

We show how to use security market data to restrict the admissible region for means and standard deviations of intertemporal marginal rates of substitution (IMRS’s) of consumers. Our approach is (i) nonparametric and applies to a rich class of models of dynamic economies; (ii) characterizes the duality between the mean-standard deviation frontier for IMRS’s and the familiar mean-standard deviation frontier for asset returns; and (iii) exploits the restriction that IMRS’s are positive random variables. The region provides a convenient summary of the sense in which asset market data are anomalous from the vantage point of intertemporal asset pricing theory.

This study argues that strong evidence contradicting the traditional assumption of time-consistent preferences is not available. The study builds and analyzes the implications of a deterministic general equilibrium model and compares them to data from the U.S. asset market. The model implies that (1) because of dynamic arbitrage, the prices of retradable assets cannot reveal whether preferences are time-inconsistent; but (2) the prices of commitment assets, investments which must be held for their lifetime, can. These prices will be higher than the present values of their future payoffs only when preferences are time-inconsistent. And (3) when preferences are time-inconsistent, people will not hold both retradable and commitment assets. Empirical observations on two examples of commitment assets—education and individual retirement accounts—are not consistent with these model implications.

This article describes a newly constructed data set of all U.S. state banks from 1782 to 1861. It contains the names and locations of all banks and branches that went into business and an estimate of when each operated. The compilation is based on reported balance sheets, listings in banknote reporters, and secondary sources. Based on these data, the article presents a count of the number of banks and branches in business by state. I argue that my series are superior to previously existing ones for reasons of consistency, accuracy, and timing. The article contains examples to support this argument.

The welfare effects of alternative monetary arrangements are computed for an economy calibrated to U.S. data. In the model world, people vary their holdings of liquid assets in order to smooth their consumption. In such worlds, we find that the feature of an arrangement that matters is the equilibrium after-tax real return on savings. We also find that relative to a tax on labor income, seigniorage is a poor source of revenue.

We study transition in a model in which the process of moving workers from matches in the state sector to new matches in the private sector takes time and involves uncertainty. When there are incentive problems in this rematching process, the optimal scheme may involve forced layoffs, involuntary unemployment, and a recession.

This paper surveys recently developed methods for Bayesian inference and their use in economic time series models. It begins by reviewing aspects of Bayesian inference essential to understanding the implications of the Bayesian paradigm for time series analysis. It next describes the use of posterior simulators to solve otherwise intractable analytical problems. The theory and the computational advances are brought together in setting forth a practical framework for decision-making and forecasting. These developments are illustrated in the context of the vector autoregressions, stochastic volatility models, and models of changing regimes.

Social learning plays an important role in models of productivity dispersion and long-run growth. In economies with a continuum of producers and unbounded productivity distributions, social learning can sometimes leave long-run growth rates completely indeterminate. This paper modifies a model in which potential entrants attempt to imitate randomly selected incumbent firms by introducing an upper bound on how much entrants can learn from incumbents. When this upper bound is taken to infinity, a unique long-run growth rate emerges, even though the economy without upper bound has an unbounded continuum of balanced growth rates.

In the data, a large fraction of price changes are temporary. We provide a simple menu cost model which explicitly includes a motive for temporary price changes. We show that this simple model can account for the main regularities concerning temporary and permanent price changes. We use the model as a benchmark to evaluate existing shortcuts that do not explicitly model temporary price changes. One shortcut is to take the temporary changes out of the data and fit a simple Calvo model to it. If we do so prices change only every 50 weeks and the Calvo model overestimates the real effects of monetary shocks by almost 70%. A second shortcut is to leave the temporary changes in the data. If we do so prices change every 3 weeks and the Calvo model produces only 1/9 of the real effects of money as in our benchmark. We show that a simple Calvo model can generate the same real effects as our benchmark model if we set parameters so that prices change every 17 weeks.

We consider the problem of an insurer who enters into a repeated relationship with a set of risk averse agents in the presence of ex post verification costs. The insurer wishes to minimize the expected cost of providing these agents a certain expected utility level. We characterize the optimal contract between the insurer and the insured agents. We then apply the analysis to the provision of deposit insurance. Our results suggest—in a deposit insurance context—that it may be optimal to utilize the discount window early on, and to make deposit insurance payments only later, or not at all.

This article studies the accuracy of two versions of Kydland and Prescott's (1980, 1982) procedure for approximating optimal decision rules in problems in which the objective fails to be quadratic and the constraints fail to be linear. The analysis is carried out using a version of the Brock-Mirman (1972) model of optimal economic growth. Although the model is not linear quadratic, its solution can nevertheless be computed with arbitrary accuracy using a variant of existing value-function iteration procedures. I find the Kydland-Prescott approximate decision rules are very similar to those implied by value-function iteration.

This paper examines the pricing of statebank notes prior to 1860 using data on the discounts on these notes as quoted in New York, Philadelphia, Cincinnati, and Cleveland. The study is organized around determining whether these banknotes were priced consistent with their expected net redemption value. It finds a bank’s notes had higher prices when it was redeeming it notes for specie than when is was suspended. However, although prices generally varied inversely with redemption costs, the relationship was not tight and persistent arbitrage opportunities existed.

We don’t really know why the U.S. banking industry is consolidating rapidly, as it has been doing for the last decade or so. After a large number of studies on the topic including this one, what seems clear is that consolidation is not producing significant efficiencies — at least not on average. Other dimensions of the consolidation trend — such as its heavy concentration in large banks — are just as poorly understood. Given this ignorance as to the “why” of consolidation, it is extremely risky to predict its future effects. Based on past experience and data, at least, we can conclude the following.

This paper describes an analytically tractable model of balanced growth that allows for extensive heterogeneity in the technologies used by firms. Firms enter with fixed characteristics that determine their initial technologies and the levels of fixed costs required to stay in business. Each firm produces a different good, and firms are subject to productivity and demand shocks that are independent across firms and over time. Firms exit when revenues are too low relative to fixed costs. Conditional on fixed firm characteristics, the stationary distribution of firm size satisfies a power law for all sizes above the size at which new firms enter. The tail of the size distribution decays very slowly if the growth rate of the initial productivity of potential entrants is not too far above the growth rate of productivity inside incumbent firms. In one interpretation, this difference in growth rates can be related to learning-by-doing inside firms and spillovers of the information generated as a result. As documented in a companion paper, heterogeneity in fixed firm characteristics together with idiosyncratic firm productivity growth can generate entry, exit, and growth rates, conditional on age and size, in line with what is observed in the data.

We derive the empirical implications of a popular class of international macroeconomic models. The real economy is a stochastic exchange model with complete markets. A standard result is that cross-country risk sharing implies perfect correlation between consumption paths across countries. With mild restrictions on the endowment process ii also implies a positive correlation between net exports and output in every country. We introduce money using cash-in-advance constraints and show that the implications for real variables carry over into the monetary economy. These dichotomy and neutrality propositions generalize those in the literature to stochastic environments with heterogeneous agents, and do not require the cash-in-advance constraint to bind in every state. They imply that any correlation between the nominal exchange rate and the balance of trade can be made consistent with the theory.

This paper proposes a theory of when labor contract should be nominal or, instead, indexed. We find that, contracts should be indexed if prices are difficult to forecast and nominal otherwise. We use a principal-agent model developed by Jovanovic and Ueda (1997), with moral hazard, renegotiation, and where a signal (the nominal value of the sales of the agent) is observed before renegotiation takes place. We show that their result, that the optimal contract is nominal when agents must choose pure strategies, is robust to the case where agents can choose mixed strategies in the sense that, for certain parameters, the optimal contract is still nominal. For other parameters, however, we show that the optimal contract is indexed. Our findings are consistent with two empirical regularities. First prices are more volatile with higher inflation and, second, countries with high inflation tend to have indexed contracts. Our theory suggests that it is because prices are difficult to forecast in high inflation countries that contracts are indexed.

We develop and calibrate a search-theoretic model of the labor market in order to forecast the evolution of the aggregate US labor market during and after the coronavirus pandemic. The model is designed to capture the heterogeneity of the transitions of individual workers across states of unemployment and employment and across different employers. The model is designed also to capture the trade-offs in the choice between temporary and permanent layoffs. Under reasonable parametrizations of the model, the lockdown instituted to prevent the spread of the novel coronavirus is shown to have long-lasting negative effects on unemployment. This is because the lockdown disproportionately disrupts the employment of workers who need years to find stable jobs.